We analyze the queueing behavior of long-tailed traffic flows under the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing, play a major role in achieving differentiated quality-of-service in integrated-services networks. We prove that, in certain scenarios, a flow may be strongly affected by the activity of `heavier'-tailed flows, and may inherit their traffic characteristics, causing induced burstiness. This phenomenon contrasts with previous results which show that, under certain conditions, an individual flow with long-tailed traffic characteristics is effectively served at a constant rate. In particular, the flow is then essentially immune from excessive activity of flows with `heavier'-tailed traffic characteristics. The sharp dichotomy in qualitative behavior illustrates the crucial importance of the weight parameters in protecting individual flows.

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CWI. Probability, Networks and Algorithms [PNA]

Borst, S.C, Boxma, O.J, & Jelenkovic, P.R. (2000). Induced burstiness in generalized processor sharing queues with long-tailed traffic flows. CWI. Probability, Networks and Algorithms [PNA]. CWI.